基于信赖域算法的精馏塔优化

doi:10.11949/0438-1157.20220036

摘要/Abstract

摘要：

从结构优化角度建立精馏塔优化的混合整数非线性规划(MINLP)模型，为了消除整数变量，引入绕流效率将MINLP问题转化为非线性规划(NLP)问题。针对得到的NLP问题提出一种优化方法，在该方法中采用结构优化中常用的信赖域优化算法进行求解，并应用虚拟瞬态连续性方程辅助优化中的稳态模拟。采用提出的优化方法对3个精馏系统进行设计优化，以不同初始值开始，均可得到令人满意的优化结果，表明所提优化方法具有良好的稳健性，对于较复杂的部分热耦合精馏过程仍然可以有效优化求解；信赖域算法在精馏塔优化中也表现出良好的收敛性。

关键词: 优化, 蒸馏, 算法, 信赖域, 绕流效率模型

Abstract:

In this paper, a mixed integer nonlinear programming (MINLP) model for distillation columns optimization is established from the perspective of structural optimization. In order to eliminate integer variables, the bypass efficiency model is introduced to transform the MINLP problem into a nonlinear programming (NLP) problem. An optimization method is proposed to solve the NLP problem. In this method, the trust region optimization algorithm which commonly used in structural optimization is used and the pseudo-transient continuation model is used to assist the steady-state simulation in optimization. The optimization method proposed in this paper is used to optimize three distillation cases. All the cases can get satisfactory optimization results starting from different initial points. The results show that the proposed optimization method has good robustness and can still effectively solve the complex partial thermal coupling distillation process. The trust region algorithm also shows good convergence in the optimization of distillation column.

Key words: optimization, distillation, algorithm, trust region, bypass efficiency model

中图分类号:

TQ 028.3

刘星伟, 贾胜坤, 罗祎青, 袁希钢. 基于信赖域算法的精馏塔优化[J]. 化工学报, 2022, 73(5): 2031-2038.

Xingwei LIU, Shengkun JIA, Yiqing LUO, Xigang YUAN. Optimization of distillation column based on trust region algorithm[J]. CIESC Journal, 2022, 73(5): 2031-2038.

图/表 11

图1 精馏塔结构参数模型示意图

Fig.1 Schematic diagram of distillation column structure parameter model

图2 绕流效率模型

Fig.2 Illustration of bypass efficiency model

图3 MMA算法

Fig.3 MMA algorithm

图4 精馏塔优化方法

Fig.4 Optimization method of distillation column

图5 乙苯-苯乙烯分离塔的结构

Fig.5 Structure of ethylbenzene-styrene column

表1 乙苯-苯乙烯分离塔的优化结果

Table 1 Optimization results of ethylbenzene-styrene column

绕流效率的初值	N₁	N₂	RR/ (kmol/kmol)	V_f/ (kmol/kmol)	TAC/ (10⁴ USD/a)
0.1	20	19	6.30	0.8348	325.445
0.3	20	19	6.30	0.8348	325.445
0.5	21	20	6.15	0.8323	327.789
0.7	20	20	6.22	0.8334	326.351
0.9	21	20	6.15	0.8323	327.789

图6 N1、N2和TAC随迭代次数的变化

Fig.6 Variation of N1, N2 and TAC with iteration

图7 直接序列精馏塔结构

Fig.7 Structure of direct sequence distillation column

表2 直接序列精馏塔的优化结果

Table 2 Optimization results of direct sequence distillation column

绕流效率的初始值	N₁	N₂	N₃	N₄	RR₁/(kmol/kmol)	V_f1/(kmol/kmol)	RR₂/(kmol/kmol)	V_f2/(kmol/kmol)	TAC/（10⁴ USD/a)
0.1	9	14	12	13	1.41	0.6124	1.50	0.7535	544.851
0.3	8	15	11	12	1.42	0.6142	1.52	0.7551	544.371
0.5	8	14	11	12	1.44	0.6142	1.53	0.7555	544.024
0.7	8	14	12	12	1.43	0.6137	1.52	0.7546	544.207
0.9	8	14	11	12	1.44	0.6142	1.53	0.7556	544.024

图8 部分热耦合精馏结构

Fig.8 Structure of partially thermally coupled distillation process

表3 部分热耦合精馏过程优化结果

Table 3 Optimization results of partially thermally coupled distillation process

绕流效率的初始值	N₁	N₂	N₃	N₄	RR₁/(kmol/kmol)	S_f/(kmol/kmol)	RR₂/(kmol/kmol)	V_f/(kmol/kmol)	TAC/(10⁴ USD/a)
0.1	8	17	11	11	2.53	0.4507	2.53	0.6611	224.098
0.3	7	17	11	11	2.56	0.4476	2.52	0.6620	224.189
0.5	7	18	10	11	2.56	0.4485	2.54	0.6631	224.328
0.7	8	18	11	11	2.51	0.4508	2.52	0.6605	224.206
0.9	7	18	10	11	2.56	0.4485	2.54	0.6631	224.328

参考文献 30

1	Kiss A A. Distillation technology-still young and full of breakthrough opportunities[J]. Journal of Chemical Technology & Biotechnology, 2014, 89(4): 479-498.
2	Cardoso M F, Salcedo R L, de Azevedo S F, et al. A simulated annealing approach to the solution of minlp problems[J]. Computers & Chemical Engineering, 1997, 21(12): 1349-1364.
3	Tsirlin A M, Balunov A I, Sukin I A. Estimates of energy consumption and selection of optimal distillation sequence for multicomponent distillation[J]. Theoretical Foundations of Chemical Engineering, 2016, 50(3): 250-259.
4	Pleşu V, Bonet Ruiz A E, Bonet J, et al. Shortcut assessment of alternative distillation sequence schemes for process intensification[J]. Computers & Chemical Engineering, 2015, 83: 58-71.
5	雷杨, 张冰剑, 陈清林. 基于MINLP的精馏塔进料板位置优化[J]. 化工进展, 2011, 30(S2): 80-84.
	Lei Y, Zhang B J, Chen Q L. Optimization of feed tray location for a distillation column based on MINLP[J]. Chemical Industry and Engineering Progress, 2011, 30(S2): 80-84.
6	姜奕. 基于混整空间粒子群算法的精馏塔优化设计[D]. 青岛: 青岛科技大学, 2015.
	Jiang Y. Optimum design of distillation column with mixed integer space particle swarm optimization algorithm[D]. Qingdao: Qingdao University of Science & Technology, 2015.
7	廖明森, 赵月红, 宁朋歌, 等. 基于MINLP模型的焦化废水蒸氨塔操作优化[J]. 过程工程学报, 2014, 14(1): 125-132.
	Liao M S, Zhao Y H, Ning P G, et al. Optimization of distillation operation for coking wastewater treatment based on MINLP model[J]. The Chinese Journal of Process Engineering, 2014, 14(1): 125-132.
8	Viswanathan J, Grossmann I E. A combined penalty function and outer-approximation method for MINLP optimization[J]. Computers & Chemical Engineering, 1990, 14(7): 769-782.
9	Ciric A R, Gu D Y. Synthesis of nonequilibrium reactive distillation processes by MINLP optimization[J]. AIChE Journal, 1994, 40(9): 1479-1487.
10	Bauer M H, Stichlmair J. Design and economic optimization of azeotropic distillation processes using mixed-integer nonlinear programming[J]. Computers & Chemical Engineering, 1998, 22(9): 1271-1286.
11	Dünnebier G, Pantelides C C. Optimal design of thermally coupled distillation columns[J]. Industrial & Engineering Chemistry Research, 1999, 38(1): 162-176.
12	Lang Y D, Biegler L T. Distributed stream method for tray optimization[J]. AIChE Journal, 2002, 48(3): 582-595.
13	Neves F J M, Silva D C M, Oliveira N M C. A robust strategy for optimizing complex distillation columns[J]. Computers & Chemical Engineering, 2005, 29(6): 1457-1471.
14	Kraemer K, Kossack S, Marquardt W. Efficient optimization-based design of distillation processes for homogeneous azeotropic mixtures[J]. Industrial & Engineering Chemistry Research, 2009, 48(14): 6749-6764.
15	袁亚湘. 信赖域方法的收敛性[J]. 计算数学, 1994, 16(3): 333-346.
	Yuan Y X. On the convergence of trust region algorithms[J]. Mathematica Numerica Sinica, 1994, 16(3): 333-346.
16	Dowling A W, Biegler L T. Rigorous optimization-based synthesis of distillation cascades without integer variables[M]//Computer Aided Chemical Engineering. Amsterdam: Elsevier, 2014: 55-60.
17	Svanberg K. The method of moving asymptotes—a new method for structural optimization[J]. International Journal for Numerical Methods in Engineering, 1987, 24(2): 359-373.
18	Svanberg K. A class of globally convergent optimization methods based on conservative convex separable approximations[J]. SIAM Journal on Optimization, 2002, 12(2): 555-573.
19	郭丽华, 汤文成, 齐文春, 等. 全局收敛移动渐近线法子问题的求解与数值验证[J]. 机械设计, 2014, 31(6): 13-17.
	Guo L H, Tang W C, Qi W C, et al. Solution and numerical verification of sub-problem of globally convergent version of MMA[J]. Journal of Machine Design, 2014, 31(6): 13-17.
20	Luo Z, Chen L, Yang J, et al. Compliant mechanism design using multi-objective topology optimization scheme of continuum structures[J]. Structural and Multidisciplinary Optimization, 2005, 30(2): 142-154.
21	Ma Y J, Luo Y Q, Yuan X G. Simultaneous optimization of complex distillation systems with a new pseudo-transient continuation model[J]. Industrial & Engineering Chemistry Research, 2017, 56(21): 6266-6274.
22	Jiang Z Y, Mathew T J, Zhang H B, et al. Global optimization of multicomponent distillation configurations: global minimization of total cost for multicomponent mixture separations[J]. Computers & Chemical Engineering, 2019, 126: 249-262.
23	Dowling A W, Gao Q W, Biegler L T. Equation-oriented optimization of cryogenic systems for coal oxycombustion power plants[M]//Proceedings of the 8th International Conference on Foundations of Computer-Aided Process Design. Amsterdam: Elsevier, 2014: 501-506.
24	Pattison R C, Gupta A M, Baldea M. Equation-oriented optimization of process flowsheets with dividing-wall columns[J]. AIChE Journal, 2016, 62(3): 704-716.
25	翟建, 刘育良, 李鲁闽, 等. 萃取精馏分离苯/环己烷共沸体系模拟与优化[J]. 化工学报, 2015, 66(9): 3570-3579.
	Zhai J, Liu Y L, Li L M, et al. Simulation and optimization of extractive distillation for separation of azeotropic benzene/cyclohexane system[J]. CIESC Journal, 2015, 66(9): 3570-3579.
26	Dejanović I, Matijašević L, Olujić Ž. Dividing wall column—a breakthrough towards sustainable distilling[J]. Chemical Engineering and Processing: Process Intensification, 2010, 49(6): 559-580.
27	Asprion N, Kaibel G. Dividing wall columns: fundamentals and recent advances[J]. Chemical Engineering and Processing: Process Intensification, 2010, 49(2): 139-146.
28	龚超, 余爱平, 罗祎青, 等. 完全能量耦合精馏塔的设计、模拟与优化[J]. 化工学报, 2012, 63(1): 177-184.
	Gong C, Yu A P, Luo Y Q, et al. Design, simulation and optimization of fully thermally coupled distillation column[J]. CIESC Journal, 2012, 63(1): 177-184.
29	Petlyuk F B, Platonov V M, Slavinskii D M. Thermodynamically optimal method of separating multicomponent mixtures[J]. Int. Chem. Eng., 1965, 5(3): 555-561.
30	Emtir M, Rév E, Mizsey P, et al. Comparison of integrated and coupled distillation schemes using different utility prices[J]. Computers & Chemical Engineering, 1999, 23: S799-S802.

[1]	杨欣, 王文, 徐凯, 马凡华. 高压氢气加注过程中温度特征仿真分析[J]. 化工学报, 2023, 74(S1): 280-286.
[2]	何松, 刘乔迈, 谢广烁, 王斯民, 肖娟. 高浓度水煤浆管道气膜减阻两相流模拟及代理辅助优化[J]. 化工学报, 2023, 74(9): 3766-3774.
[3]	陈哲文, 魏俊杰, 张玉明. 超临界水煤气化耦合SOFC发电系统集成及其能量转化机制[J]. 化工学报, 2023, 74(9): 3888-3902.
[4]	曹跃, 余冲, 李智, 杨明磊. 工业数据驱动的加氢裂化装置多工况切换过渡状态检测[J]. 化工学报, 2023, 74(9): 3841-3854.
[5]	齐聪, 丁子, 余杰, 汤茂清, 梁林. 基于选择吸收纳米薄膜的太阳能温差发电特性研究[J]. 化工学报, 2023, 74(9): 3921-3930.
[6]	邢雷, 苗春雨, 蒋明虎, 赵立新, 李新亚. 井下微型气液旋流分离器优化设计与性能分析[J]. 化工学报, 2023, 74(8): 3394-3406.
[7]	张曼铮, 肖猛, 闫沛伟, 苗政, 徐进良, 纪献兵. 危废焚烧处理耦合有机朗肯循环系统工质筛选与热力学优化[J]. 化工学报, 2023, 74(8): 3502-3512.
[8]	诸程瑛, 王振雷. 基于改进深度强化学习的乙烯裂解炉操作优化[J]. 化工学报, 2023, 74(8): 3429-3437.
[9]	尹刚, 李伊惠, 何飞, 曹文琦, 王民, 颜非亚, 向禹, 卢剑, 罗斌, 卢润廷. 基于KPCA和SVM的铝电解槽漏槽事故预警方法[J]. 化工学报, 2023, 74(8): 3419-3428.
[10]	陈国泽, 卫东, 郭倩, 向志平. 负载跟踪状态下的铝空气电池堆最优功率点优化方法[J]. 化工学报, 2023, 74(8): 3533-3542.
[11]	刘文竹, 云和明, 王宝雪, 胡明哲, 仲崇龙. 基于场协同和耗散的微通道拓扑优化研究[J]. 化工学报, 2023, 74(8): 3329-3341.
[12]	吴文涛, 褚良永, 张玲洁, 谭伟民, 沈丽明, 暴宁钟. 腰果酚生物基自愈合微胶囊的高效制备工艺研究[J]. 化工学报, 2023, 74(7): 3103-3115.
[13]	汤晓玲, 王嘉瑞, 朱玄烨, 郑仁朝. 基于Pickering乳液的卤醇脱卤酶催化合成手性环氧氯丙烷[J]. 化工学报, 2023, 74(7): 2926-2934.
[14]	文兆伦, 李沛睿, 张忠林, 杜晓, 侯起旺, 刘叶刚, 郝晓刚, 官国清. 基于自热再生的隔壁塔深冷空分工艺设计及优化[J]. 化工学报, 2023, 74(7): 2988-2998.
[15]	高学金, 姚玉卓, 韩华云, 齐咏生. 基于注意力动态卷积自编码器的发酵过程故障监测[J]. 化工学报, 2023, 74(6): 2503-2521.